I'm designing an HF transmitter/transceiver and need to ensure that there are no harmonics/spurs attenuated less than 50 dBc (that is, 50 dB below the carrier, as required by the US FCC). But I'm new to all this involves. I understand the theory behind a Spectrum Analyzer. But I've never actually used one. For purposes such as mine will the StemLab 125-10 Spectrum Analyzer (not calibrated!) do what I need? Or should I plan to also budget for a hardware device such as the Rigol DSA815-TG? A more elaborate/sophisticated Spectrum Analyzer than the Rigol is simply not within my budgetary means.

Red Pitaya's dynamic is at least 80 dB (and could reach more than 110 dB under certain circumstances/software/filtering). It's far enough to use it for a two tone test

Anyhow, don't be focused on a detail like the testing of your final amplifier. Very few hams are using spectrum or scalar analyzers. It would be counterproductive to buy a more than 3000 US$ piece of equipment for just one measure.
You'll probably need quite a lot of other gears to build your rig. Certainly a good volmeter, RLC meter, RF generator, milliwattmeter (and this is the minimum entry ticket). A VNA would be a good thing, depending on your budget.

with such an equipment and some simulation softwares, you'll be able to reach more than your aimed 50 dB of rejection (by the way, the RP itself can be used as a transmitter with a far better 3rd order product). A VNA would tell you, for example, the rejection of your low pass filter, generally around 80 to 120 dB (more if you use Cauer topology), thus allowing to easily reach your "50 dB goal".

with new generation SDR including pre-distorsion and envelope elimination/restitution techniques (EER), 80 % of the linerarity problems are purely software dependant. An A.S. will be of little help from this point of view
My2cts
marc f6itu